%I #6 Feb 22 2013 14:40:25

%S 1,0,1,0,3,1,0,4,6,1,0,4,17,9,1,0,4,32,39,12,1,0,4,48,111,70,15,1,0,4,

%T 64,240,268,110,18,1,0,4,80,432,769,530,159,21,1,0,4,96,688,1792,1905,

%U 924,217,24,1,0,4

%N Riordan array (1, x*(1+x)^2/(1-x)).

%C Triangle T(n,k), read by rows, given by (0, 3, -5/3, 4/15, -3/5, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%C Row sums are A077995(n).

%F T(2*n,n) = A119259(n).

%F G.f.: (1-x)/(1-(1+y)*x-2*y*x^2-y*x^3).

%F T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k-1) + T(n-3,k-1), T(0,0) = 1, T(1,0) = 0.

%e Triangle begins :

%e 1

%e 0, 1

%e 0, 3, 1

%e 0, 4, 6, 1

%e 0, 4, 17, 9, 1

%e 0, 4, 32, 39, 12, 1

%e 0, 4, 48, 111, 70, 15, 1

%e 0, 4, 64, 240, 268, 110, 18, 1

%e 0, 4, 80, 432, 769, 530, 159, 21, 1

%e 0, 4, 96, 688, 1792, 1905, 924, 217, 24, 1

%e 0, 4, 112, 1008, 3584, 5503, 3999, 1477, 284, 27, 1

%e 0, 4, 128, 1392, 6400, 13440, 13842, 7483, 2216, 360, 30, 1

%Y Cf. Diagonals : A000012, A008585, A022266, A000007, A113311

%K easy,nonn,tabl

%O 0,5

%A _Philippe Deléham_, Feb 17 2012